There is a very curious vulgar error which prevails, even among people who have a good practical acquaintance with arithmetic. It is that the number _ten_ has some special virtue which fits it for counting up to. The fact is that ten is not the best number for the purpose; you can halve it, it is true, but that is about all you can do with it, for its being divisible by five is of hardly any use for practical purposes. _Eight_ would be a much better number, for you can halve it three times in succession; and _twelve_ is perhaps the most convenient number possible, as it will divide by two, three, and four. It is this convenient property that leads tradesmen to sell by dozens, and grosses, rather than by tens and hundreds. If we used eights or twelves instead of tens for numeration, we might of course preserve all the advantages of the Indian or Arabic numerals; in the first case, we should discard the ciphers 8 and 9, and reckon 5, 6, 7, 10; and in the second case, we should want two new ciphers for ten and eleven; and 10 would stand for twelve, and 11 for thirteen. Our happening to have ten fingers has really led us into a rather inconvenient numerical system. [Illustration: AZTEC HEAD, IN TERRA COTTA. (PROBABLY EITHER A HOUSEHOLD-GOD OR A VOTIVE OFFERING).] CHAPTER V. MEXICO. GUADALUPE. [Illustration: The Rebozo worn by the Women of Mexico; and the Serape worn by the Men.] While we were away at the Real del Monte, the news had reached Mexico that Puebla had capitulated, and that the rebel leader had fled. The victory was celebrated in the capital with the most triumphal entries, harangues, bull-fights, and illuminations done to order. If you had a house in one of the principal streets, the police would make you illuminate it, whether you liked or not. The newspapers loudly proclaimed the triumph of the constitutional principle, and the inauguration of a reign of law and order that was never to cease. As for the newspapers, indeed, one looked in vain in them for any free expression of public opinion. They were all either suppressed, or converted into the merest mouthpieces of the government. The telegraph was under the strictest surveillance, and no messages were allowed to be sent which the government did not consider favourable to their interests; a precaution which rather defeated itself, as the people soon ceased to believe any public news at all. In all these mean little shifts, which we in England consider as the special property of despotic governments, the authorities of the Mexican Republic showed themselves great proficients. We were left, therefore, to form what idea we could of the real state of Mexican affairs, from the private information received by our friends. Just for once it may be worth while to give a few details, not because the people engaged were specially interesting, but because the affair may serve to give an idea of the condition of the country.